Problem: $A$ $B$ $C$ If: $ AC = 28$, $ AB = 4x + 6$, and $ BC = 5x + 4$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 6} + {5x + 4} = {28}$ Combine like terms: $ 9x + 10 = {28}$ Subtract $10$ from both sides: $ 9x = 18$ Divide both sides by $9$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $BC$ $ BC = 5({2}) + 4$ Simplify: $ {BC = 10 + 4}$ Simplify to find ${BC}$ : $ {BC = 14}$